But even Reid had to thank on-loan keeper Steve Banks for a remarkable win after he pulled off an amazing double penalty save deep in injury time to secure Bradford's first victory since September 14.
Bradford looked to be coasting after Reid rifled in his second after 55 minutes but Norwich launched a ferocious fightback and only Banks' wonder save denied them a point.
With all hands to the pump as City hung on referee Paul Danson pointed to the spot after Danny Cadamarteri sent Steen Nedergaard sprawling in the box.
Canaries skipper Iwan Roberts fired a right-foot penalty low to Banks' right but he superbly pushed the ball away and then plunged at Roberts' feet as he followed up.
Amazingly the close-range effort hit Banks' body and looped over the bar from inside the six-yard box.
It was a final dramatic let-off for Bradford who had already survived a series of scares in a thrilling second half.
Reid, who had only made one substitute appearance so far this season, made his mark with a stunning strike four minutes before the end of a scrappy first half.
When Norwich could only half clear Stephen Warnock's corner Reid picked his spot from 30 yards out and unleashed a sensational right-foot drive which rocketed into the visitors net.
At the start of the second half Norwich keeper Robert Green had to show his best to deny Cadamarteri twice within the space of a minute but he could nothing when Bradford skipper Ashley Ward laid the ball off for unlikely hero Reid to fire in his second from 14 yards.
Bradford wasted further chances before Norwich launched their revival following a double substitution.
Substitute Zema Abbey headed them back into the contest after 70 minutes when he rose highest to meet Nicky Southall's corner and Green pulled off another incredible stop to keep out a close-range effort from Ward.
Banks showed all his agility to keep out efforts from Abbey and substitute Paul Heckingbottom before his late heroics secured a much-needed win for the home side.